Coal rock interface identification method based on improved DS evidence theory

Abstract

The invention provides a coal rock interface identification method based on an improved DS evidence theory, and belongs to the technical field of data analysis and multi-source information fusion. A plurality of information source signals in the cutting process are collected; constructing a recognition framework; obtaining a basic probability distribution function of each information source for elements in the recognition framework through the triangular fuzzy number and the trapezoidal fuzzy number; fusing the basic probability distribution function of each information source by using a Dempster combination rule, including introducing a conflict degree, a difference degree and a dispersion degree to define a new evidence conflict coefficient; correcting the evidence body according to the new evidence conflict coefficient; and based on the fused basic probability distribution function, selecting an element with the maximum probability in the recognition framework as a recognition result. According to the method, the application of a multi-source information fusion algorithm in engineering practice is realized, and compared with the traditional DS evidence theory, the method can more comprehensively reflect the relationship between evidence bodies, reduce the conflict between the evidence bodies and improve the accuracy of an identification result.

Description

Technical Field

[0001] The invention relates to the technical field of data analysis and multi-source information fusion, and in particular to a coal-rock interface recognition method based on improved DS evidence theory. Background Art

[0002] The automatic, fast and accurate identification of the drum cutting state during coal mining is of great significance to mine safety, production efficiency, equipment maintenance and other aspects. At present, the drum cutting state is often judged by manual experience, which has the hidden dangers of high danger, strong subjectivity and low accuracy. Therefore, it is proposed to monitor the changes of cutting state through sensors; however, there are a lot of noise, abnormal values, missing values ​​and other factors in the coal mining process, which are easy to interfere with the cutting signal. A single monitoring signal may conflict with the actual result, and it is impossible to accurately judge the cutting state of the coal mining machine. It is necessary to improve its identification method.

[0003] In view of this, it is proposed to use multiple sensors for detection. However, there may be conflicts in the recognition results between multiple sensors. In the prior art, the influence of different sensors on the recognition results can be comprehensively analyzed through the theory of multi-source information fusion. Among them, DS evidence theory is a widely used multi-source information fusion method. However, in the prior art, the calculation of the conflict coefficient K in DS evidence theory often describes the conflict between evidence from the degree of conflict, which cannot fully reflect the relationship between evidence, resulting in an increase in the possibility of inconsistency and mutual exclusivity between evidence. This leads to differences in the sensitivity of different sensors to cutting the same substance, and sometimes even conflicts in the recognition results, which are completely contrary to the facts.

[0004] Therefore, a coal-rock interface identification method is needed to improve the accuracy of sensor information fusion. Summary of the invention

[0005] In view of this, the present invention provides a coal-rock interface identification method based on improved DS evidence theory. DS evidence theory is used to analyze multi-source signals collected in the cutting experiment, improve the DS conflict coefficient, reduce the conflict degree between evidence bodies, and improve the accuracy of judging the cutting state of the coal mining machine.

[0006] To this end, the present invention provides the following technical solutions:

[0007] A coal-rock interface identification method based on improved DS evidence theory includes:

[0008] Collect multiple information source signals during the cutting process;

[0009] Build a recognition framework;

[0010] The basic probability distribution function of each information source for the elements in the recognition framework is obtained through triangular fuzzy numbers and trapezoidal fuzzy numbers;

[0011] Using Dempster's combination rule, the basic probability distribution function of each information source is integrated;

[0012] Based on the fused basic probability distribution function, the element with the highest probability in the recognition frame is selected as the recognition result;

[0013] The Dempster combination rule is used to fuse the basic probability distribution functions of different information sources, including:

[0014] Introduce conflict degree, difference degree and dispersion degree to define a new evidence conflict coefficient;

[0015] Modify the body of evidence according to the new evidence conflict coefficient.

[0016] Furthermore, the multiple information source signals include:

[0017] Current signals, acoustic emission signals and vibration signals.

[0018] Furthermore, the identification framework:

[0019] Θ = {coal, rock, interface, gangue}.

[0020] Furthermore, the basic probability distribution function of each information source for the elements in the recognition framework is obtained by using the triangular fuzzy number and the trapezoidal fuzzy number, including:

[0021] Constructing the membership function of different elements in each information source based on the characteristic signal distribution of different elements in each information source;

[0022] Fuzzy numbers are defined according to the membership functions of different elements in each information source, and a triangular fuzzy number model for each information source is constructed:

[0023]

[0024] Among them, A ij , B ij , C ij Respectively represent the minimum, average, and maximum values ​​of the elements monitored by information source j. i The matrix constructed for training samples under category i, the row vector represents the value of each training sample on k attributes, and the column vector represents m training samples;

[0025] The basic probability assignment function is generated through triangular fuzzy numbers.

[0026] Furthermore, the Dsmpster combination rule is used to fuse the basic probability distribution function:

[0027]

[0028] Furthermore, the introduction of conflict degree, difference degree and dispersion degree to define a new evidence conflict coefficient includes:

[0029] Evidence conflict parameter S mm′ (X l ):

[0030]

[0031] Among them, α mm′ (X l ), λ mm′ (X l ), μ mm′ (X l ) represent the conflict degree, difference degree and discrete degree of the lth sensor between the mth and m′th monitoring cycles respectively;

[0032] Conflict degree α mm′ (X l ):

[0033] α mm′ (X l )=K mm′ (X l )=∑ m≠m′ (m lm ×mμ lm′ )

[0034] Among them, K mm′ (X l ) is the conflict coefficient between the lth sensor in the mth and mμ′ monitoring cycles, mμ lm 、mμ lm′ are the basic probability distribution functions of the lth sensor in the mth and m′th monitoring periods, respectively;

[0035] Difference λ mm’ (X l ) 2 :

[0036]

[0037] Among them, d mm′ (X l ) jousselme represents the Jousselme distance between the mth and m′th monitoring periods of the lth sensor; Respectively represent the vectorization of the mass function of the lth sensor in the mth and m′th monitoring cycles; d mm′ (X l ) Pignistic represents the Pignistic distance between the lth sensor in the mth and m′th monitoring periods; BetPm The total probability of a sub-event in P(Θ) is the support for the sub-event; |A| represents the cardinality of event A;

[0038] Discreteness μ mm′ (X l ): It is expressed by focusing degree μ, which indicates the uncertainty of a single body of evidence. The larger μ is, the smaller the uncertainty is.

[0039]

[0040] 0≤μ mm′ (X l )≤1

[0041] Among them, μ mm′ (X l ) represents the focusing degree of the lth sensor between the mth and m′th monitoring cycles.

[0042] Furthermore, the step of modifying the body of evidence according to the new evidence conflict coefficient includes:

[0043] pass Normalize the conflict parameters and calculate the difference matrix ξ(X l ) and the credibility matrix η(X l ):

[0044] η(X l )=1-ξ(X l )

[0045]

[0046] The correction coefficient of the lth sensor in the mth detection cycle is τ m (X l ):

[0047]

[0048] Combined correction factor η(X l ) To amend the body of evidence:

[0049]

[0050] Among them, η m (X l ) represents the total credibility of the lth sensor in the mth monitoring cycle.

[0051] Furthermore, obtaining the characteristic signal distribution of different elements in each information source includes:

[0052] Construct a multi-source clipping signal dataset;

[0053] Preprocessing the multi-source clipping signal data set;

[0054] Based on the preprocessed data set, the characteristic indicators of multi-source cutting signals are extracted by sliding window;

[0055] Through Pearson correlation analysis and sensitivity analysis, the characteristic indicators of multi-source cutting signals are screened to obtain characteristic signals;

[0056] The characteristic signals include: the root mean square value of the vibration signal in the X / Y / Z axis, the average value of the current signal, and the order of magnitude of the energy count of the acoustic emission signal.

[0057] Furthermore, the data set preprocessing includes:

[0058] Align multi-source signal data according to time series, and fill missing values ​​with the mean of adjacent data;

[0059] Mean filtering is used to reduce the interference of noise on the cutting signal.

[0060] Advantages and positive effects of the present invention:

[0061] The present invention realizes the application of multi-source information fusion algorithm in engineering practice. Compared with the traditional DS evidence theory, it can more comprehensively reflect the relationship between evidence bodies, reduce the conflict between evidence bodies, and improve the accuracy of recognition results. At the same time, the improved DS evidence theory can be applied to other multi-source information fusion fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0063] Figure 1 A flow chart of a method in an embodiment of the present invention;

[0064] Figure 2 A multi-source data acquisition system in an embodiment of the present invention;

[0065] Figure 3 The coal and rock samples with different cutting ratios in the similar simulation experiment in the embodiment of the present invention;

[0066] Figure 4 This is a heat map of correlation coefficient analysis of feature vectors in an embodiment of the present invention;

[0067] Figure 5This is a framework diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0068] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0069] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0070] The present invention provides a coal-rock interface recognition method based on improved DS evidence theory. The method collects coal-rock cutting state information of coal mining machine based on current, acoustic emission and vibration sensors; processes and analyzes multi-source cutting signals, and constructs characteristic data sets of coal, rock, gangue and interface respectively; extracts characteristic indicators for different substances; improves the calculation method of conflict coefficient in DS evidence theory, and corrects the relationship between evidence bodies from the perspectives of conflict degree, difference degree and discrete degree. The current, acoustic emission and vibration characteristic indicators are integrated to obtain coal-rock recognition results.

[0071] Combination Figure 1 The flow chart shown further illustrates the method of the present invention:

[0072] S1, build feature data set;

[0073] Based on experimental acquisition of multi-source signals;

[0074] The multi-source signal data are aligned according to the time series, and the missing values ​​are filled by the mean of the adjacent data; mean filtering is used to reduce the interference of noise on the cut signal, and the preprocessed data set is used as the basis for extracting feature indicators.

[0075] Based on the preprocessed data, a multi-source data set of four different conditions, coal, rock, interface, and gangue, was constructed. The sliding window method was used to extract data feature indicators, and the sliding window length was finally determined to be 5 and the number of moving steps was 1. The extracted feature indicators include: mean value, standard deviation, sample kurtosis, sample kurtosis, and wavelet coefficient. Furthermore, through Pearson correlation analysis (such as Figure 4 ) and sensitivity analysis, the root mean square value of the vibration signal X / Y / Z axis, the average value of the current signal, and the order of magnitude of the energy counts of the acoustic emission signal are selected as characteristic signals.

[0076] S2, build recognition framework;

[0077] In this embodiment, the elements in the frame Θ include coal, rock, interface, and gangue:

[0078] Θ={coal, rock, interface, gangue}

[0079] S3, using Dempster combination rule to integrate basic probability distribution functions;

[0080] In DS evidence theory, the distribution characteristics of data determine the basic probability distribution function of the evidence body. The function values ​​of different evidence bodies are solved, and the basic probability distribution functions of multi-source feature signals are fused using the Desmpster combination rule.

[0081] Basic probability distribution function: Fuzzy numbers are defined based on the membership function of the elements. Common fuzzy numbers include triangular fuzzy numbers and trapezoidal fuzzy numbers. In this embodiment, the information sources include: current signal, vibration signal, and acoustic emission signal. The m data in event A can be used as training samples, and each training sample can be represented by three information sources. Therefore, X ij Represents the value of a training sample in category i on attribute j, and constructs a matrix containing all training samples belonging to category i as expression E i :

[0082]

[0083] in It is the value of the current information source in the coal sample data set with respect to the training sample.

[0084] Establish triangular fuzzy number models with different information sources:

[0085]

[0086] Among them, A ij , B ij , C ij Respectively represent the minimum, average, and maximum values ​​of the elements monitored by information source j. iThe matrix constructed for training samples under category i, the row vector represents the value of each training sample on k attributes, and the column vector represents m training samples.

[0087] The basic probability assignment function (BPA) is generated through triangular fuzzy numbers.

[0088] Using the Dsmpster combination rule, the basic probability distribution function BPA is integrated:

[0089]

[0090] The new evidence conflict coefficient is defined by introducing the conflict degree, difference degree and dispersion degree to describe the mutual correlation, fuzziness and difference among multi-source feature signals.

[0091] New evidence conflict parameter S mm′ (X l ):

[0092]

[0093] Conflict degree α mm′ (X l ):

[0094] α mm′ (X l )=K mm′ (X l )=∑ m≠m′ (m lm ×m lm′ )

[0095] Difference λ mm’ (X l ) 2 :

[0096]

[0097] Discreteness μ mm′ (X l ):

[0098]

[0099] The new conflict coefficient After normalization, the difference matrix between the evidence bodies of the lth sensor in each monitoring period is obtained as ξ(X l ) and the credibility matrix, η(X l )=1-ξ(X l ).

[0100]

[0101] Evidence correction coefficient τ for the mth detection cycle of the lth sensor m (X l )for:

[0102]

[0103] Combined correction factor η(X l ), and modify the body of evidence:

[0104]

[0105] S4. Select the data with the highest probability after fusion as the recognition result.

[0106] In this embodiment S1, information is collected through experiments to construct a feature data set. Figure 5 The specific process is as follows:

[0107] According to the cutting mechanism of the coal mining machine and the failure process of the coal-rock interface, the main parameters affecting the preparation of the coal-rock specimens are determined as follows: the total load P of the coal mining machine pick, the compressive strength σ of the coal-rock simulation specimen, the elastic modulus E, the Poisson's ratio μ, the strain ε, the bulk density ρ, the gravitational acceleration G, and the characteristic size l; the similarity criterion is constructed according to the similarity criterion, the dimensions of each parameter about the mass M, length L, and time T are extracted, and the dimensional index matrix is ​​constructed. The results are shown in Table 1; and the dimensional vectors of the parameters σ, P, and E are converted into unit vectors, the unit matrix of the dimensional index is constructed, and the similarity constant C is solved. P , C E , C μ , C ε , C σ , C ε .

[0108] Among them, similarity criteria:

[0109] π4=μ,π5=ε

[0110] Table 1

[0111] σ P E ρ g l M 1 1 1 1 0 0 L -1 1 -1 -3 1 1 T -2 -2 -2 0 -2 0 <![CDATA[π1]]> 1 0 0 -1 -1 -1 <![CDATA[π2]]> 0 1 0 -1 -1 -3 <![CDATA[π3]]> 0 0 1 -1 -1 -1

[0112] Solve for the similarity constant C P , C E , C μ , C ε , C σ ,

[0113]

[0114] C E =C ρ ·C G ·Cl =C ρ ·C l

[0115] C μ =1, C ε =1

[0116] C σ =C ρ ·C g ·C l =C ρ ·C l

[0117] C ε =1; C μ =1;

[0118] Combined with the mechanical properties and similarity constants of the research area (roof, coal seam, interlayer, floor) in the mine geological report, the mechanical properties of the simulated sample are calculated. The distortion coefficient (combined with the joints of the coal rock in the mine) is introduced to correct the difference in mechanical properties between the natural sample and the simulated sample due to different joints and fissures. In the experiment, the compressive strength of the simulated coal sample is 2.25 times that of the natural coal sample, and the compressive strength of the simulated rock sample is 1.3 times that of the natural rock sample. Multiplying it with the similarity constant, the mechanical properties of the simulated sample after distortion are obtained.

[0119] The materials required for preparing coal samples are determined to be: coal powder, cement, gypsum, and water; the materials required for rock samples are: river sand, cement, gypsum, and water. Before the experiment, similar materials need to be dried and uniformly screened according to particle size to ensure the uniformity of the sample. According to the mechanical properties of the simulated sample, the ratio range of similar materials is determined, and uniaxial mechanical experiments are carried out to determine the size of the mechanical properties of the simulated sample, and the ratio of similar materials is selected.

[0120] Coal-rock cutting samples were prepared according to the obtained similar material ratio. In the process of preparing coal samples, in order to ensure the flatness of the coal-rock interface, the rock sample area in the mold was first filled with foam board; in order to ensure the uniformity of the sample, the coal sample was poured three times, and the bubbles in the coal sample were discharged by vibration during the pouring process; in order to ensure the consistency of the size of the sample after preparation, the pouring thickness was 2-3cm higher than the designed thickness of the specimen. After the preparation is completed, in order to prevent the surface cracking caused by the inconsistent evaporation rate of the surface and internal water of the coal sample, the surface of the coal sample is sprayed with water every 8 hours. After the coal sample reaches the initial setting strength, the foam board in the rock sample area is removed, and the cement slurry is prepared in proportion and applied to the coal-rock interface surface at the coal sample. After the slurry penetrates into the coal sample, the rock sample is poured three times. The steps for pouring the rock sample are the same as those for the coal sample. After pouring, it is cured at room temperature for 21 days.

[0121] Coal rock sample cutting experiment:

[0122] After the specimen is cured and formed, it is demoulded and the left, right and rear sides of the specimen are fixed on the test bench. According to the predetermined cutting path, the cutting height of the shearer drum is adjusted for cutting. The distance between the shearer cutting drum and the coal rock specimen is fixed, and the cutting depth of the cutting drum is 10 cm to ensure that the shearer has a consistent cutting depth during the movement; connect the power supply of the test bench to run the shearer cutting and walking mechanisms at the same time. Determine the signal acquisition system (such as Figure 2 The installation position, collected data parameters, collection channel position, etc. of the current sensor, acoustic emission sensor and vibration acceleration sensor are shown in the figure.

[0123] After the preparation work is completed, start the cutting drum of the coal mining machine, wait for the drum speed to stabilize, and start the coal mining machine operating mechanism, current sensor, acoustic emission sensor and vibration acceleration sensor at the same time, in order to ensure the normal operation of the signal acquisition system during the rotation and movement of the coal mining machine. When the traveling mechanism runs to the stop position, first stop the drum rotation, and finally close the current sensor, acoustic emission sensor and vibration acceleration sensor acquisition channels. For coal and rock samples with different cutting ratios (such as Figure 3 As shown), repeat the above steps and the multi-source signal data acquisition is completed.

[0124] The present invention can characterize the coal-rock interface in complex forms through similar simulation experiments, and realize the diversity, randomness and similarity of the coal-rock interface. The feasibility of multi-source information fusion algorithm in coal-rock cutting experimental data collection, data processing and recognition effect is determined. The improved DS evidence theory can reduce the conflict between different evidence bodies and improve the accuracy and reliability of coal-rock interface recognition.

[0125] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A coal-rock interface identification method based on improved DS evidence theory, characterized in that: include: Collect multiple information source signals during the cutting process; Build a recognition framework; The basic probability distribution function of each information source for the elements in the recognition framework is obtained through triangular fuzzy numbers and trapezoidal fuzzy numbers; Using Dempster's combination rule, the basic probability distribution function of each information source is integrated; Based on the fused basic probability distribution function, the element with the highest probability in the recognition frame is selected as the recognition result; The Dempster combination rule is used to fuse the basic probability distribution functions of different information sources, including: Introduce conflict degree, difference degree and dispersion degree to define a new evidence conflict coefficient; Modify the body of evidence according to the new evidence conflict coefficient.

2. According to the coal-rock interface identification method based on improved DS evidence theory as described in claim 1, it is characterized in that: The multiple information source signals include: Current signals, acoustic emission signals and vibration signals.

3. According to the coal-rock interface identification method based on improved DS evidence theory as described in claim 1, it is characterized in that: The identification framework: Θ = {coal, rock, interface, gangue}.

4. According to the coal-rock interface identification method based on improved DS evidence theory as described in claim 1, it is characterized in that: The basic probability distribution function of each information source for the elements in the identification framework is obtained by using the triangular fuzzy number and the trapezoidal fuzzy number, including: Constructing the membership function of different elements in each information source based on the characteristic signal distribution of different elements in each information source; Fuzzy numbers are defined according to the membership functions of different elements in each information source, and a triangular fuzzy number model for each information source is constructed: Among them, A ij , B ij , C ij Respectively represent the minimum, average, and maximum values ​​of the elements monitored by information source j. i The matrix constructed for training samples under category i, the row vector represents the value of each training sample on k attributes, and the column vector represents m training samples; The basic probability assignment function is generated through triangular fuzzy numbers.

5. According to the coal-rock interface identification method based on improved DS evidence theory as described in claim 1, it is characterized in that: The Dsmpster combination rule is used to integrate the basic probability distribution function:

6. The coal-rock interface identification method based on improved DS evidence theory according to claim 1 is characterized in that: The introduction of conflict degree, difference degree and dispersion degree to define a new evidence conflict coefficient includes: Evidence conflict parameter S mm′ (X l ): Among them, α mm′ (X l ), λ mm′ (X l ), μ mm′ (X l ) represent the conflict degree, difference degree and discrete degree of the lth sensor between the mth and m′th monitoring cycles respectively; Conflict degree α mm′ (X l ): α mm′ (X l )=K mm′ (X l )=∑ m≠m′ (m lm ×m lm′ ) Among them, K mm′ (X l ) is the conflict coefficient between the lth sensor in the mth and m′th monitoring cycles, m lm 、m lm′ are the basic probability distribution functions of the lth sensor in the mth and m′th monitoring periods, respectively; Difference λ mm’ (X l ) 2 : Among them, d mm′ (X l ) jousselme represents the Jousselme distance between the mth and m′th monitoring periods of the lth sensor; Respectively represent the vectorization of the mass function of the lth sensor in the mth and m′th monitoring cycles; d mm′ (X l ) Pignistic represents the Pignistic distance between the lth sensor in the mth and m′th monitoring periods; BetP m The total probability of a sub-event in P(Θ) is the support for the sub-event; |A| represents the cardinality of event A; Discreteness μ mm′ (X l ): It is expressed by focusing degree μ, which indicates the uncertainty of a single body of evidence. The larger μ is, the smaller the uncertainty is. 0≤μ mm′ (X l )≤1 Among them, μ mm′ (X l ) represents the focusing degree of the lth sensor between the mth and m′th monitoring cycles.

7. The coal-rock interface identification method based on improved DS evidence theory according to claim 1 is characterized in that: The step of modifying the body of evidence according to the new evidence conflict coefficient includes: pass Normalize the conflict parameters and calculate the difference matrix ξ(X l ) and the credibility matrix η(X l ): the(X l )=1-ξ(X l ) The correction coefficient of the lth sensor in the mth detection cycle is τ m (X l ): Combined correction factor η(X l ) To amend the body of evidence: Among them, η m (X l ) represents the total credibility of the lth sensor in the mth monitoring cycle.

8. According to the coal-rock interface identification method based on improved DS evidence theory as described in claim 4, it is characterized in that: Obtaining characteristic signal distribution of different elements in each of the information sources, including: Construct a multi-source clipping signal dataset; Preprocessing the multi-source clipping signal data set; Based on the preprocessed data set, the characteristic indicators of multi-source cutting signals are extracted by sliding window; Through Pearson correlation analysis and sensitivity analysis, the characteristic indicators of multi-source cutting signals are screened to obtain characteristic signals; The characteristic signals include: the root mean square value of the vibration signal in the X / Y / Z axis, the average value of the current signal, and the order of magnitude of the energy count of the acoustic emission signal.

9. A coal-rock interface identification method based on improved DS evidence theory according to claim 8, characterized in that: The data set preprocessing includes: Align multi-source signal data according to time series, and fill missing values ​​with the mean of adjacent data; Mean filtering is used to reduce the interference of noise on the cutting signal.

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